US2024255380A1PendingUtilityA1
Methods for determining the cyclostationnarity of a vibration signal relating to a mechanical system, for arranging vibration sensors for monitoring such a system, and for monitoring it
Est. expiryJan 30, 2043(~16.5 yrs left)· nominal 20-yr term from priority
G01M 13/028G01H 1/12G01H 1/003
51
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Claims
Abstract
A method for determining the cyclostationarity of a vibration signal transmitted by a vibration sensor arranged on a mechanical system and allowing a cyclostationarity indicator Iα to be calculated. The present disclosure also relates to a method for arranging vibration sensors, using the method for determining cyclostationarity applied to the signals transmitted by these vibration sensors at different positions and orientations. A position of a vibration sensor is validated as a function of this cyclostationarity indicator Iα. The present disclosure finally relates to a method for monitoring a mechanical system 10 using the method for determining cyclostationarity to determine the cyclostationarity of the vibration signals relating to the mechanical system before calculating the monitoring indicators of the mechanical system.
Claims
exact text as granted — not AI-modifiedWhat is claimed is:
1 . A method for determining the cyclostationarity of a vibration signal relating to a mechanical system, the mechanical system comprising at least one rotating member that rotates about a rotation axis, at least one vibration sensor transmitting the temporal vibration signal s(t), an angular sensor transmitting a temporal angular signal θ(t) that varies as a function of an angular position of the rotating member about the rotation axis, and a calculator,
the method comprising the following steps:
transforming the temporal vibration signal s(t) into an angular vibration signal s(θ), using the calculator, as a function of the temporal angular signal θ(t);
using the calculator to calculate a normalized cyclostationarity indicator I α using a statistical hypothesis test and as a function of the angular vibration signal s(θ); and
determining that the angular vibration signal s(θ) is cyclostationary when the cyclostationarity indicator I α is greater than or equal to a predetermined cyclostationarity threshold, the predetermined cyclostationarity threshold being between 0 and 1,
for which the method is intended to determine cyclostationarity of order 1, and the statistical hypothesis test is a Student's test applied to an estimate {circumflex over (m)}(θ) of a synchronous mean of the angular vibration signal s(θ) in relation to a cyclic period Φ and the calculation of a cyclostationarity indicator I α comprises an intermediate step of determining a statistical indicator η α (θ) calculated according to the following relationship:
η
α
(
θ
)
=
t
α
K
-
1
.
σ
^
(
θ
)
K
,
wherein t α K-1 is half of a confidence interval associated with the Student's test with K−1 degrees of freedom with a risk 1α;
{circumflex over (σ)}(θ) is an estimate of the standard deviation of the angular vibration signal s(θ) corresponding to a normal distribution for an angle θ defined such that
σ
^
(
θ
)
=
(
θ
)
.
K
K
-
1
;
θ is the angular position of the rotating member about the rotation axis;
(θ) is an estimate of the synchronous variance of the angular vibration signal s(θ) in relation to the cyclic period Φ, such that
(
θ
)
=
1
K
∑
i
=
0
K
-
1
[
r
^
(
θ
+
i
.
Φ
)
]
2
;
{circumflex over (r)}(θ) is an estimate of a residual of the angular vibration signal s(θ) such that {circumflex over (r)}(θ)=s(θ)−{circumflex over (m)}(θ);
{circumflex over (m)}(θ) is the estimate of the synchronous mean in relation to the cyclic period Φ such that
m
^
(
θ
)
=
1
K
∑
i
=
0
K
-
1
s
(
θ
+
i
.
Φ
)
;
√{square root over ( )} is the square root function;
Σ is the sum function;
Φ is the cyclic period of the angular vibration signal s(θ);
K is a number of cycles such that
K
=
N
Φ
;
N is a number of sampling points forming the angular vibration signal s(θ); and
i is an integer varying from 0 to (K−1).
2 . The method according to claim 1 ,
for which the cyclostationarity indicator I α is calculated using the following relationship:
I
α
=
∑
θ
(
❘
"\[LeftBracketingBar]"
m
^
(
θ
)
❘
"\[RightBracketingBar]"
.
𝒥
Cyc
(
θ
)
)
∑
θ
❘
"\[LeftBracketingBar]"
m
^
(
θ
)
❘
"\[RightBracketingBar]"
,
wherein Cyc (θ) is an indicator function of the cyclostationarity of the angular vibration signal s(θ) that is equal to 1 if {circumflex over (m)}(θ)>η α (θ) and equal to 0 if {circumflex over (m)}(θ)≤η α (θ); and
∥ is the absolute value function.
3 . The method for determining the cyclostationarity of a vibration signal relating to a mechanical system, the mechanical system comprising at least one rotating member that rotates about a rotation axis, at least one vibration sensor transmitting the temporal vibration signal s(t), an angular sensor transmitting a temporal angular signal θ(t) that varies as a function of an angular position of the rotating member about the rotation axis, and a calculator,
the method comprising the following steps:
transforming the temporal vibration signal s(t) into an angular vibration signal s(θ), using the calculator, as a function of the temporal angular signal θ(t);
using the calculator to calculate a normalized cyclostationarity indicator I α using a statistical hypothesis test and as a function of the angular vibration signal s(θ); and
determining that the angular vibration signal s(θ) is cyclostationary when the cyclostationarity indicator I α is greater than or equal to a predetermined cyclostationarity threshold, the predetermined cyclostationarity threshold being between 0 and 1,
for which the method is intended to determine cyclostationarity of order 2 and the statistical hypothesis test is Bartlett's test applied to an estimate of a synchronous variance of the angular vibration signal s(θ) in relation to a cyclic period Φ and the cyclostationarity indicator I α is calculated according to the following relationship:
I
α
=
exp
(
-
x
α
2
ψ
)
,
wherein exp is the exponential mathematical function;
ψ is a scalar determined as a function of the estimate of the synchronous variance such that:
ψ
=
3
N
.
(
K
-
1
)
.
[
ln
(
∑
n
=
1
N
(
θ
n
)
/
N
)
-
∑
n
=
1
N
ln
(
(
θ
n
)
)
/
N
]
3
N
.
(
K
-
1
)
+
N
+
1
;
(θ) is the estimate of the synchronous variance in relation to the cyclic period Φ, such that
(
θ
)
=
1
K
∑
i
=
0
K
-
1
[
r
^
(
θ
+
i
.
Φ
)
]
2
;
{circumflex over (r)}(θ) is an estimate of a residual of the angular vibration signal s(θ) such that {circumflex over (r)}(θ)=s(θ)−{circumflex over (m)}(θ);
{circumflex over (m)}(θ) is an estimate of the synchronous mean of the angular vibration signal s(θ) in relation to the cyclic period Φ, such that
m
^
(
θ
)
=
1
K
∑
i
=
0
K
-
1
s
(
θ
+
i
.
Φ
)
;
Σ is the sum function;
θ is the angular position of the rotating member about the rotation axis;
Φ is the cyclic period of the angular vibration signal s(θ);
K is a number of cycles such that
K
=
N
Φ
;
N is a number of sampling points forming the angular vibration signal s(θ);
i is an integer varying from 0 to (K−1);
ln is the natural logarithm function; and
α 2 is a confidence interval associated with a chi-squared distribution with (N−1) degrees of freedom with a risk 1−α.
4 . The method according to claim 1 ,
for which the method comprises at least one of the following additional steps:
generating a cyclostationarity alert when the cyclostationarity indicator I α is greater than or equal to the cyclostationarity threshold; and
generating a non-cyclostationarity alert when the cyclostationarity indicator I α is less than the cyclostationarity threshold.
5 . An arrangement method for arranging at least one vibration sensor dedicated to monitoring a mechanical system, the mechanical system comprising at least one rotating member that rotates about a rotation axis, at least one vibration sensor, an angular sensor, and a calculator,
the arrangement method comprising the following steps carried out over at least two successive iterations:
positioning and orienting the vibration sensor (s) on the mechanical system, the vibration sensor (s) being situated in a different position and/or orientation at each iteration;
transmitting a temporal vibration signal s(t) by means of the vibration sensor (s), for different operating modes of the mechanical system;
transmitting a temporal angular signal θ(t), by means of the angular sensor, that varies as a function of an angular position of the rotating member about the rotation axis for the different operating modes of the mechanical system; and
calculating a cyclostationarity indicator I α relative to the temporal vibration signal s(t) for the different operating modes of the mechanical system, by applying the method for determining cyclostationarity according to claim 1 ,
the arrangement method also comprising a step of validating the position and the orientation of the vibration sensor (s) on the mechanical system, wherein the position and the orientation of the vibration sensor(s) are validated if a characteristic value of the cyclostationarity indicators I α relating to the position and the orientation for the different operating modes of the mechanical system is greater than a validation threshold, the characteristic value being chosen from a median value of the cyclostationarity indicators I α , an arithmetic mean of the cyclostationarity indicators I α or a root mean square of the cyclostationarity indicators I α .
6 . The method according to claim 5 ,
for which, during the validation step, the position and the orientation of the vibration sensor (s) are validated if a difference between a maximum value and a minimum value of the cyclostationarity indicators I α relating to the position and the orientation is also less than a difference threshold.
7 . The method according to claim 6 ,
for which the difference threshold is equal to a percentage of the characteristic value of the cyclostationarity indicators I α .
8 . The method according to claim 5 ,
for which the different operating modes of the mechanical system comprise only stabilized operating modes and do not comprise transient operating modes.
9 . The method for monitoring a mechanical system, the mechanical system comprising at least one rotating member that rotates about a rotation axis, at least one vibration sensor transmitting one temporal vibration signal x(t), an angular sensor transmitting a temporal angular signal θ(t) that varies as a function of an angular position of the rotating member about the rotation axis, and a calculator,
the method comprising the following steps:
transmitting the temporal vibration signal s(t) by means of the vibration sensor (s);
transmitting the temporal angular signal θ(t) by means of the angular sensor;
calculating a cyclostationarity indicator I α for the temporal vibration signal s(t), by applying the method for determining cyclostationarity according to claim 1 ;
if the cyclostationarity indicator I α is greater than or equal to the cyclostationarity threshold, calculating at least one monitoring indicator of the mechanical system, with the calculator, as a function of the temporal vibration signal s(t); and
determining the presence of a fault in the mechanical system by comparing the monitoring indicator (s) with a fault threshold.
10 . The method according to claim 9 ,
for which the presence of a fault in the mechanical system is determined if the monitoring indicator (s) is/are greater than the fault threshold.
11 . The method according to claim 9 ,
for which the monitoring indicator (s) comprise (s) the cyclostationarity indicator I α or is calculated as a function of the cyclostationarity indicator I α .
12 . A device for determining cyclostationarity for validating whether a temporal vibration signal x(t) relating to a mechanical system is cyclostationary, the validation device being configured for a mechanical system comprising at least one rotating member that rotates about a rotation axis and at least one vibration sensor transmitting the temporal vibration signal s(t), the device for determining cyclostationarity comprising an angular sensor transmitting a temporal angular signal θ(t) that varies as a function of an angular position of the rotating member about the rotation axis, and a calculator,
wherein the device for determining cyclostationarity is configured to implement the method according to claim 1 .
13 . A device for arranging at least one vibration sensor dedicated to monitoring a mechanical system, the mechanical system comprising at least one rotating member that rotates about a rotation axis, at least one vibration sensor, the arrangement device comprising an angular sensor transmitting a temporal angular signal θ(t) that varies as a function of an angular position of the rotating member about the rotation axis, and a calculator,
wherein the arrangement device is configured to implement, over at least two successive iterations, the steps of transmitting a temporal vibration signal s(t) by means of the vibration sensor (s) for different operating modes of the mechanical system, of transmitting a temporal angular signal θ(t) by means of the angular sensor, and of calculating a cyclostationarity indicator I α relative to the temporal vibration signal s(t) for the different operating modes of the mechanical system of the method according to claim 5 , the at least one vibration sensor is located at a different position and/or orientation at each iteration, the arrangement device being next configured to implement the step of validating the position and the orientation of the vibration sensor (s) on the mechanical system.
14 . A monitoring device for monitoring a mechanical system, the monitoring device being configured to monitor a mechanical system comprising at least one rotating member that rotates about a rotation axis, the monitoring device comprising at least one vibration sensor transmitting a temporal vibration signal s(t), an angular sensor transmitting a temporal angular signal θ(t) that varies as a function of an angular position of the rotating member about the rotation axis, and a calculator,
wherein the monitoring device is configured to implement the method according to claim 9 .
15 . A mechanical system comprising at least one rotating member that rotates about a rotation axis,
wherein the mechanical system comprises the monitoring device according to claim 14 .
16 . A gearbox comprising the mechanical system according to claim 15 .Join the waitlist — get patent alerts
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